计算几何评定圆度的方法研究

和传统方法相比,计算几何方法评定圆度误差几何直观性强、结果准确,而且能解决同时存在多个最小径向间距MRS(Minimum RadialSeparation)圆心的问题.按照被测轮廓的表示,该方法可分为两类:一类是用被测工件表面上取的样本点来近似地表示该轮廓;另一类是用这些样本点产生一个简单多边形来表示该轮廓.这两种方法确定的内接圆是不同的.文章对比分析了它们的适用性、精度和计算效率以及存在的问题.     

计算几何在测试计量技术中的应用-求解最小外接圆

提供一种在机械科学中评定最小外接圆柱形状误差的高效、高精度算法。该算法的核心是提出了一种删除对求解最小外接圆不会起任何作用的无关样本点的有效方法。交替运用计算几何中的最远点Voronoi图的性质和统计分析方法撮小二乘法原理,可使最后参与求解最小外接圆的样本点数减至少量几个,相应算法的运算时间比以往的最优化快10倍以上。     

基于计算几何的直线度评定法

提出了一种用计算几何方法来评定直线度误差的算法，并以实例加以验证，同时和以往算法进行了比较。新方法不仅提供了在理论上严格符合公差定义中关于“最小区域”的定义的精确解，而且计算速度快，其时间复杂度公为O（N）。     

基于计算几何和遗传算法的直线度误差评定

针对机械工程测量中常见的直线度误差评定问题,本文建立了基于计算几何和遗传算法的最小区域素线直线度误差评定算法。并利用VB编写了相应的评定模块,采用多组数据对两种算法的评定结果和效率进行了比较。结果表明,遗传算法的评定结果与计算几何算法相近,但计算几何算法更稳定、效率更高,且可以得到符合国家标准定义的最小区域直线度误差值。     

一种基于最远Voronoi图的最小外接圆求解方法

当测量平面上一组测量点集的外接圆圆心在该点集的最远Voronoi图上移动时,对应的外接圆半径具有单调收敛性,并收敛于该点集的最小外接圆圆心.根据该性质,提出了一种基于最远Voronoi图的最小外接圆求解方法.编制了相应的算法程序,设计了验证方法,并与穷举法进行了比较,测试结果表明利用该方法进行圆度误差评定不存在误差累积,且具有线性时间复杂度.     

回转体零件轮廓度误差评定方法的实用数学模型研究

本文从实用需要出发,研究提出一种快速而且实用的直接根据最小区域原理来评定回转体轮廓度误差的数学模型。还提出了另一种便于实用的最小二乘评定方法数学模型。     

圆度误差评定的迭代法计算实例

阐述了迭代法评定圆度误差的原理、方法和步骤,并结合实例将迭代的过程制成计算表格,简单清晰、方便使用.     

大型工件平面度平行度垂直度误差计算与评定方法

提出了一种实用的大型工件平面度、平行度、垂直度误差的计算与评定方法。这种方法适用于各种不规则、不连续的测量表面。评定程序采用最小二乘和最小条件法，搜素速度快，评定结果精度高。     

最大内接圆法评定圆度误差值的快速、精确算法

介绍了利用最大内接圆判别准则求解圆度误差的基本思想,论述了用最大内接圆法评定圆度误差值的快速、精确算法。利用本文所述的计算方法,能够设计出圆度误差评定软件,实现三坐标测量数据的圆度误差评定。     

自由边界平面连通域的Voronoi图生成方法研究

平面连通域的Vorono,图被广泛应用于许多领域,常用的分治法等算法实现较为复杂,影响了其应用范围在凸多边形中轴算法的基础上,提出一种建立自由边界平面连通域的Voronoi图的新方法.通过求解相邻边界元素的平分线,计算出相邻平分线的交点,由距离最小的平分线交点实现Voronoi图边的增长,最终建立完整的平面单连通域的Voronoi图.同时,还介绍了平面多连通域的内外边界的Voronoi图的合并算法.     

Hexahedral mesh generation by medial surface subdivision: Part I. Solids with convex edges

A method is presented for subdividing a large class of solid objects into topologically simple subregions suitable for automatic finite element meshing with hexahedral elements. The technique uses a geometric property of a solid, its medial surface, to define the necessary subregions. The subregions are defined explicitly to be one of only 13 possible types. The subdividing cuts are between parts of the object in geometric proximity and produce good quality meshes of hexahedral elements. The method as introduced here is applicable to solids with convex edges and vertices, but the extension to complete generality is feasible.     

HEXAHEDRAL MESH GENERATION BY MEDIAL SURFACE SUBDIVISION: PART II. SOLIDS WITH FLAT AND CONCAVE EDGES

A method is presented for the subdivision of a large class of solids into simple subregions suitable for automatic finite element meshing with hexahedral elements. The medial surface subdivision technique described previously in the literature is used as the basis for this work and is extended here to cover solids which have flat and concave edges. Problems where the medial surface is degenerated are also addressed. © 1997 by John Wiley & Sons, Ltd.     

A method to design biomimetic scaffolds for bone tissue engineering based on Voronoi lattices

In regenerative medicine, 3D scaffolds are used to sustain the regeneration of tissues in removed or damaged parts of the human body. As such practices are being widely experimented in clinical applications, the design, the materials and the manufacturing process to obtain efficient 3D biocompatible lattices are being significantly investigated. Nevertheless, most of the proposed designs are based on regular 3D shapes obtained from the repetition of unit cells disposed in a three-dimensional array. This approach does not exploit the whole potential of computer-aided design tools coupled with manufacturing capabilities for freeform shapes. In this paper, we propose a method to model biomimetic lattices controlling the porosity and the pores size of scaffolds to be integrated with the anatomical shape of the defect. The method has been implemented in bone tissue case study and implements a generative design approach based on Voronoi diagrams.     

Cellular topology optimization on differentiable Voronoi diagrams

Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric representation to characterize the system's spatially varying cellular evolution driven by objective sensitivities. A conventional discrete cellular structure, for example, a Voronoi diagram, whose representation relies on discrete Voronoi cells and faces, lacks its differentiability to facilitate large-scale, gradient-based topology optimizations. We propose a topology optimization algorithm based on a differentiable and generalized Voronoi representation that can evolve the cellular structure as a continuous field. The central piece of our method is a hybrid particle-grid representation to encode the previously discrete Voronoi diagram into a continuous density field defined in a Euclidean space. Based on this differentiable representation, we further extend it to tackle anisotropic cells, free boundaries, and functionally-graded cellular structures. Our differentiable Voronoi diagram enables the integration of an effective cellular representation into the state-of-the-art topology optimization pipelines, which defines a novel design space for cellular structures to explore design options effectively that were impractical for previous approaches. We showcase the efficacy of our approach by optimizing cellular structures with up to thousands of anisotropic cells, including femur bone and Odonata wing.     

MATNET: A neural network for medial axis transformation

Abstract

This paper describes a novel neural network, called MATNET, to perform the medial axis transformation which is often used to extract a stick‐figure‐like representation from a binary object for pattern analysis or recognition. The MATNET is derived from the structure of the retina, which consists of five neural layers, namely, receptors, horizontal cells, bipolar cells, ganglion cells, and response. In principle, the horizontal cell is implemented for distance computation; the bipolar cell (B‐net) and the ganglion cell (G‐net) are implemented for calculation of local minimum and local maximum, respectively. The B‐net and G‐net are concerned with the maximal neural network (Maxnet). The properties of Maxnet are also discussed. Experimental results show that the MATNET performs reasonably.     

Automatic and efficient hybrid viscous mesh generation based on clipped Voronoi diagrams

The commonly used advancing layers method to generate hybrid meshes suffers from many drawbacks. The generation of isotropic meshes for far-field domains with irregular and complex boundary subdivisions after boundary layers advancing is time consuming and, in some cases, is not robust in 3D. To address these difficulties, this paper presents a novel method to generate hybrid polygonal meshes in 2D and polyhedral meshes in 3D for viscous flow simulations. In the proposed method, first, we generate a full Voronoi diagram for the appropriate distribution of generators that avoids the extra mesh generation required for the remaining holes in the advancing layers method. To recover the inner solid boundaries, we implement a robust boundary cell cutting process. Because the generators are located layer by layer near the boundaries, there is no requirement to consider all of the Voronoi cells. Only the first layer Voronoi cells must be cut, making the calculation very efficient. We have generated hybrid meshes using the present method for many viscous flow cases. The results show close agreement between the computations and the experimental results, thus indicating the reliability and effectiveness of the hybrid mesh generated by our method.